Dynamical simulation via quantum machine learning with provable generalization

Abstract

Much attention has been paid to dynamical simulation and quantum machine learning (QML) independently as applications for quantum advantage, while the possibility of using QML to enhance dynamical simulations has not been thoroughly investigated. Here we develop a framework for using QML methods to simulate quantum dynamics on near-term quantum hardware. We use generalization bounds, which bound the error a machine learning model makes on unseen data, to rigorously analyze the training data requirements of an algorithm within this framework. This provides a guarantee that our algorithm is resource-efficient, both in terms of qubit and data requirements. Our numerics exhibit efficient scaling with problem size, and we simulate 20 times longer than Trotterization on IBMQ-Bogota.

arXiv commentMain text: 5 pages & 3 Figures. Supplementary Information: 12 pages & 2 Figures

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• Classically estimating observables of noiseless quantum circuits
• Complexity of quantum circuits via sensitivity, magic, and coherence
• Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metric
• Lie-algebraic classical simulations for quantum computing
• Transition Role of Entangled Data in Quantum Machine Learning
• Large-scale simulations of Floquet physics on near-term quantum computers
• Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Survey
• Variational quantum computing for quantum simulation: principles, implementations, and challenges
• The power and limitations of learning quantum dynamics incoherently
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits
• Quantum neural compressive sensing for ghost imaging
• Deep Circuit Compression for Quantum Dynamics via Tensor Networks
• High-fidelity dimer excitations using quantum hardware
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• Feedback-Based Quantum Strategies for Constrained Combinatorial Optimization Problems
• Disentangling quantum autoencoder
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